How do people get away without understanding?

[jd12345]

Ok so here I am studying - trying to understand the concepts and ideas behind something. Well some of the guys in the class just race through it. I am surprised as it seemed like a really difficult and abstract concept to get your mind around.

When asked for help I realized that they didn't truly understand the concept. However it was sufficient for them to score marks and ace through the exam.
Why is this? I spent a whole lot of time understanding the concept and I guess I have a much better understanding than them.

But in the exams, you can get away without understanding the idea behind it. Why?

I sometimes feel frustrated wasting my time to get my head around a particular idea while others just learn how to solve problems realted to the concept and the basic know-how

 

[Ryan_m_b]

It's important to manage one's time. Completely understanding everything isn't always desirable. Often there is little practical advantage to knowing more about something than how to use it, for instance: when performing a series of experiments someone with mostly functional knowledge could perform just as well as someone with total and have far more time to study other things.

Obviously this is not always the case but this is worth bearing in mind.

 

[jd12345]

It's important to manage ones time. Completely understanding everything isn't always desirable. Often there is little practical advantage to knowing more about something than how to use it, for instance: when performing a series of experiments someone with mostly functional knowledge could perform just as well as someone with total and have far more time to study other things.

Obviously this is not always the case but this is worth bearing in mind.

This is exactly what is happening. This is my first year in college and I am having this difficulty.
In school I had plenty of time to get deep into the subjects and understand them well. In college I'm unable to find this time but still trying to get deep. While others have the all-important functional knowledge they do pretty well in exams while I'm still in a half-knowledge state.

I find it difficult to leave the core idea behind and just focus on the main functional knowledge of the subject.

 

[Fizicks1]

I feel the same as you. In my college, many people just focus on doing problems and past papers, and not on understanding a lot of the deeper conceptual ideas to the physics.

I on the other hand tend to prefer really understanding the concepts and I often end up not having enough time to work through enough problems for all my courses.

A few friends of mine who likes to focus on working through problems usually score higher than I do on exams, but when asked more conceptual questions from others, they occasionally make quite unreasonable conceptual mistakes. For example, one of them said (in quantum mechanics) that a linear combination of stationary states still in general satisfies the time independent Schrodinger equation.

So, I don't know, I'd say strike a balance between the two. You don't want to spend all your time understanding all the underlying concepts, and as a result leave no time for doing practice problems. On the other hand, you don't want to be the guy who has pretty poor understanding but grinds through tons of practice problems and only knows how to regurgitate answers during exams.

 

[jimmyly]

http://youtu.be/u5iVP-07Lm8

Very interesting video about physics education. A professor did some physics education research on Harvard pre-med students and found that students who understand conceptually tend to do better than students who just memorize steps to solve problems.

 

[Square1]

Ok so here I am studying - trying to understand the concepts and ideas behind something. Well some of the guys in the class just race through it. I am surprised as it seemed like a really difficult and abstract concept to get your mind around.

When asked for help I realized that they didn't truly understand the concept. However it was sufficient for them to score marks and ace through the exam.
Why is this? I spent a whole lot of time understanding the concept and I guess I have a much better understanding than them.

But in the exams, you can get away without understanding the idea behind it. Why?

I sometimes feel frustrated wasting my time to get my head around a particular idea while others just learn how to solve problems realted to the concept and the basic know-how

You don't know how much this torments me. Curiosity can become an impediment at times. And what's worse is when you ask these people for explanations and they say something to the extent of "just because" or basically just regurgitate the notes back to you word for word not letting a single toe step out beyond the bounds of the notes. I've found this observation so counterintuitive as to what I thought university would be about...that it would filter out for the people the love to sink their teeth into the material, and those that would plan on learning just what is needed for assignments, labs and such...but I've seen that it doesn't work like that in undergrad. Maybe someone with more experience could say when or if it does become like that.

Often there is little practical advantage to knowing more about something than how to use it, for instance: when performing a series of experiments someone with mostly functional knowledge could perform just as well as someone with total and have far more time to study other things.

Obviously this is not always the case but this is worth bearing in mind.

Another reason you could give yourself is that you should trust that the tests your profs make are fulfilling the learning requirements and just trust this system. What if next semester you take a class that changes the way you thought you understood the concept from last semester. What would you think of your understanding at that point? For example, you probably thought you understood the structure of an atom some time in junior high or high school with all those nice routine circular electron orbits. By the time you graduated high school I bet exposure to quantum chemistry changed that.

Things like this have helped me although I find it hard to accept. Also is a bit of a change in learning style too. Hope this helps you.

 

[jimmyly]

Another reason you could give yourself is that you should trust that the tests your profs make are fulfilling the learning requirements and just trust this system.QUOTE]

In the video I posted, The professor at one point talks about how tests are written. He made up a test with a few conceptual questions and the remaining were practical questions and the majority of students got it wrong. Some students even asked him when they will be doing "real" physics, as in solving practical problems. He found that the students who understood the material conceptually also did well with practical problems, BUT the students who memorized steps for practical problems failed the conceptual questions. There is a lot more to it, I have just took little bits of parts.

After watching this video I've realized that its very hard to analyze how much you know by looking at grades because of how some exams and tests are made.

 

[MathematicalPhysicist]

I've found this observation so counterintuitive as to what I thought university would be about...that it would filter out for the people the love to sink their teeth into the material, and those that would plan on learning just what is needed for assignments, labs and such...but I've seen that it doesn't work like that in undergrad. Maybe someone with more experience could say when or if it does become like that.

As you grow up, most of the stuff you once thought will be seen as fantasies.

Welcome to the real world, where what's important is who scores more, is faster, makes better grades, publish more, etc etc...

 

[cryora]

In my opinion, understanding something in depth will more likely help you out in the long run, because you'll be able to retain the material and remember the details that others may have missed, and as a result, you'll do better in future classes.

An example is gravitational potential energy. It is tempting to think, "oh that's easy, I'll just use the equation U = -GMm/r." A dedicated learner would want to know how it is derived, and that is no easy task because you have to keep track of any arbitrarily assumptions made, all of the negative signs that get multiplied together during the calculation and why each negative sign exist.

Let's see how potential energy changes as the force of gravity from an object with mass M acts on an object of mass m.
ΔU = Uf - Ui
= - W ..... (1)
= - Integral ri to rf F.dr
= - Integral ri to rf -Fdr ...... (2)
= - Integral ri to rf -GMm/r^2 dr
= -(-GMm) * Integral ri to rf 1/r^2 dr
= - (-GMm) * (-1/r) | ri to rf ........ (3)
= -(-GMm)(-1)(1/rf - 1/ri)
= -GMm(1/rf - 1/ri)
Setting Ui = 0 as ri -> infinity
Uf = -GMm/rf

3 negative signs arose during the calculation.
(1) comes from the fact that the change in gravitational potential energy is the opposite of the work done by gravity
(2) comes from the fact that the force of gravity F acts opposite the direction of the displacement vector r, or 180 degress, thus their dot product is negative
(3) comes from integrating 1/r^2

Understanding how gravitational potential energy is going to be useful in learning electrostatic potential energy, which is derived in a similar way, but adds new a twist where whether the force is attractive or repulsive depends on the charge on each particle.

 

[jimmyly]

In my opinion, understanding something in depth will more likely help you out in the long run, because you'll be able to retain the material and remember the details that others may have missed, and as a result, you'll do better in future classes.

An example is gravitational potential energy. It is tempting to think, "oh that's easy, I'll just use the equation U = -GMm/r." A dedicated learner would want to know how it is derived, and that is no easy task because you have to keep track of any arbitrarily assumptions made, all of the negative signs that get multiplied together during the calculation and why each negative sign exist.

Let's see how potential energy changes as the force of gravity from an object with mass M acts on an object of mass m.
ΔU = Uf - Ui
= - W ..... (1)
= - Integral ri to rf F.dr
= - Integral ri to rf -Fdr ...... (2)
= - Integral ri to rf -GMm/r^2 dr
= -(-GMm) * Integral ri to rf 1/r^2 dr
= - (-GMm) * (-1/r) | ri to rf ........ (3)
= -(-GMm)(-1)(1/rf - 1/ri)
= -GMm(1/rf - 1/ri)
Setting Ui = 0 as ri -> infinity
Uf = -GMm/rf

3 negative signs arose during the calculation.
(1) comes from the fact that the change in gravitational potential energy is the opposite of the work done by gravity
(2) comes from the fact that the force of gravity F acts opposite the direction of the displacement vector r, or 180 degress, thus their dot product is negative
(3) comes from integrating 1/r^2

Understanding how gravitational potential energy is going to be useful in learning electrostatic potential energy, which is derived in a similar way, but adds new a twist where whether the force is attractive or repulsive depends on the charge on each particle.

i agree with this. I find if i know more about what I'm studying i can solve a wider range of problems given to me whether or not i have seen them in the past or not. Also, in my perspective, the difference between understanding and following a step by step recipe is what separates the good from the great.

 

[Mentalist]

I will agree with cryora in this and, personally, I am like the OP. I feel without understanding, I am actually doing myself a disservice. Grades aren't important as they merely communicate what you can do with the material given, the more practical side of what is needed to pass the course with an adequate enough of a grade. But that doesn't mean those that pass with A's really understood the material at hand, some do understand faster and get it. However, not understanding and passing with an A because of tricks of memorizing patterns will not help you in the long run. It means that the knowledge of the material isn't strong, and because of that the knowledge will dissipate and more than likely if you are one of those people, will forget things. In other words, if you don't understand the material, the practical nature of how to work out a problem will be lost as time goes by.

It will be much better for you later on in life when you are doing research that requires you to think and go on what you understand. Gaps in knowledge or understanding won't allow you to go further in your research. But don't allow your grades to slide because of a mediocre system either (I don't like the structure of school, not saying your school is mediocre, I just dislike grading in general).

For me, I work out some of the toughest problems of the material I can find (not a lot, just some over a few days). Even if I don't get the right answer, with close deliberation I get a better understanding of the material and that to me is much better than getting the right answer without much forethought placed into thinking.

I also don't believe in the practice of doing lots and lots of problems. To me that is backwards and is too much work. It is better if you work smarter by doing only tough problems. That is what you will deal with mostly and if you do many easy to medium level difficult problems, when the tougher problems come creeping you may find yourself pushing it aside because you are tired or don't have much time to focus on them. Always start with the tougher problems and think them through based on what you know.

More than likely if you can workout the toughest problems, you will pass the tests with A's. Instructors generally put conceptual questions that can be tough and workout problems that are more moderate in difficulty. Some may put 1 hard question, but if you've been solving the hardest problems (usually back-end of the book or using a tougher text as a studying tool) the concept questions won't be hard to solve nor will the workout problems.

I can relay the strategy I use to study though.

I usually read the chapter first (no notes). I then, after reading, summarize everything etc..., and usually have a question or two (not a lot). Just a simple paragraph or so of what was done. I then look for some tougher problems to do, I used Kleppner as a problem go to book when I needed the tougher problems as the physics department had his book on their shelves and was recommended by a professor that said if I wanted to kill myself go for it. I usually had the book open and worked out the problems with open book and some thoughts.

By doing that I knew misconceptions I held, what information I knew and didn't know so well, so it was easy for me to fill the gaps instead of taking a test and then figuring what I didn't know all too well, its better to be proactive. If I did lots of problems starting from the beginning I would possibly still not have understood the material and learned how to solve the problems based on pattern recognition. Pattern recognition is good and all but not at the cost of what you WANT to do. Usually that is what it means, "do lots of problems" = do many problems so recognize patterns to pass the test.